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Classical Liquids in Fractal Dimension.

Marco Heinen1, Simon K Schnyder2, John F Brady1

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters
|September 16, 2015
PubMed
Summary

We introduce fractal liquids, generalizing classical liquids to noninteger dimensions. These fractal liquids, composed of fractal particles, exhibit unique thermodynamic and correlation behaviors studied via simulation.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Complex Systems

Background:

  • Classical liquids are typically described in integer dimensions (d=1, 2, 3).
  • Fractal structures and configurations are observed in various physical systems, including liquids in porous media and gels.
  • Generalizing liquid properties to fractal dimensions is an open area of research.

Purpose of the Study:

  • To introduce and define the concept of fractal liquids with noninteger dimensions.
  • To investigate the thermodynamic properties and pair correlations of these fractal liquids.
  • To validate theoretical models against simulation data for fractal liquids.

Main Methods:

  • Development of a generic model system for fractal liquids.
  • Utilizing computer simulations to study fractal liquids composed of fractal hard spheres on a percolating lattice cluster.
  • Employing semianalytical statistical mechanics, including the fractal Percus-Yevick liquid integral equation.

Main Results:

  • Demonstration of fractal liquids with noninteger dimensions (dl).
  • Characterization of thermodynamic behavior and pair correlations in fractal liquids.
  • Successful comparison between simulation results and predictions from the fractal Percus-Yevick integral equation.

Conclusions:

  • Fractal liquids represent a valid generalization of classical liquids to noninteger dimensions.
  • The studied model provides insights into the behavior of complex liquid systems.
  • The fractal Percus-Yevick equation accurately predicts the behavior of fractal liquids within the studied model.